light and matter
DESCRIPTION
School of Physics & Astronomy University of Southampton. Light and Matter. Controlling light with light. Tim Freegarde. is a tensor of rank. potential is anharmonic for large displacements. Optical nonlinearity. restoring force is nonlinear function of displacement. - PowerPoint PPT PresentationTRANSCRIPT
Light and MatterTim Freegarde
School of Physics & Astronomy
University of Southampton
Controlling light with light
2
Optical nonlinearity• potential is anharmonic for large displacements
43220
2cxbxxmxV
x 332210 EEEP
• polarization consequently varies nonlinearly with field
xVdd
• restoring force is nonlinear function of displacement
xV
• is a tensor of rank n 1n
3
Electro-optic effect
• nonlinearity mixes static and oscillatory fields
332210 EEEP
x
xVdd
EEEP 320
20
10 32
• exploit the nonlinear susceptibility
• Pockels (linear) and Kerr (quadratic) effects
0E
• consider withEEE 0 0EE
4
Pockels (linear electro-optic) effect
x
xVdd
• nonlinearity mixes static and oscillatory fields
0E
EEχEχP 021
0 0,: 02 ,0: EEχ
• applying intrinsic permutation symmetry, 0
21 0,:21 Eχχε 2
03 0,0,:3 Eχ
• in non-centrosymmetric materials, dominates
2χ
5
Kerr (quadratic electro-optic) effect
x
xVdd
• nonlinearity mixes static and oscillatory fields
0E
EEχEχP 021
0 0,: 02 ,0: EEχ
• applying intrinsic permutation symmetry,
021 0,:21 Eχχε
20
3 0,0,:3 Eχ • in centrosymmetric materials, 02 χ
6
Second harmonic generation
x
xVdd
332210 EEEP
• again exploit the nonlinear susceptibility
• distortion introduces overtones (harmonics) 221
0 EEP
where 22cos1cos 22 tEtE
• consider strong field EE
7
Second harmonic generation
x
xVdd
• generated intensities depend upon square of fundamental intensity
• incident field: fundamental• constant
component:optical
rectification• new frequency: second
harmonic
• focussed and pulsed beams give higher conversion efficiencies
• non-centrosymmetric materials required
8
Second harmonic generation
x
xVdd
i
iEE
• if the fundamental field contains differently polarized components
then the harmonic field contains their products
ijjiji EEχP ,:3
203
• the harmonic polarization need not be parallel to ,iE jE
9
Sum and difference frequency generation
x
xVdd
i
iEE
• if the fundamental field contains different frequency components
then the harmonic field contains their products
ijji ji EEχP ,:3
203
where ji 3
10
Pockels cell
polarizer
polarizermodulation voltage
• voltage applied to crystal controls birefringence and hence retardance• mounted between crossed linear polarizers
• longitudinal and transverse geometries for modulation field• allows fast intensity modulation and beam switching
11
Sideband generation2V• bias Pockels cell to
VVT2
sin 2
tVV 10 cos
Pockels cell
V0 V
V1
trans
miss
ion
• add r.f. field to modulate transmitted intensity
• transmitted field contains sum and difference frequency sidebands
0 0 10 10
12
Harmonic generation• fields may be at optical, radio or quasistatic
frequencies 2• combines in pairs, to produce sums and
differences• higher terms in susceptibility may combine more
frequencies• frequency tripling, quadrupling• high harmonic generation
• total photon energy conserved:
ener
gy
1 2 3 43214 e.g.
13
Phase matching• transit time through crystal x
l
cxlxt 2• harmonic beam is superposition of
contributions from all positions in crystal• for contributions to emerge in phase, 2
• use birefringence to offset dispersion 2• choose opposite polarizations for and 2
• conservation of photon momentum
14
Faraday (magneto-optic) effect
• consider effect of longitudinal field upon bound electrons
2220
2
20
3
cmNeV
• optical properties may also be influenced by magnetic fields
B
magneto-optical glass
• induced circular birefringence, characterized by Verdet constant
• non-reciprocal
15
Quantum description of atomic polarization
x/a0 x/a0
1,2exp1,0
tit
r
1 2
• electron density depends upon relative phase of superposition components
16
Faraday optical isolator
• optical ‘diode’ passes incident light but rejects reflection
polarizer
polarizermagneto-
optical glass
B
• 45º rotation in permanent magnetic field
• http://physics.nadn.navy.mil/physics/faculty/mungan/scholarship/FaradayIsolators.pdf